The dynamics of a large number of electrons is described by various approximation models depending on the physical scale under consideration. At the microscopic level (atoms, molecules, nanostructures), the Hartree-Fock system provides fairly accurate predictions [1]}, [2]}, [3]}, [4]}. On the other hand, at the larger mesoscopic level (gases), microscopic models are reduced to kinetic ones such as Vlasov, Boltzmann, Fokker-Planck type equations, and they are employed for computational efficiency. In particular, the Vlasov-Poisson system is rigorously derived as a semi-classical limit from the Hartree-Fock equation [5]}, [6]}, [7]}, [8]}, [9]}.
